What is the Greatest Common Factor of 38205 and 38210?

Greatest common factor (GCF) of 38205 and 38210 is 5.

GCF(38205,38210) = 5

We will now calculate the prime factors of 38205 and 38210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38205 and 38210.

How to find the GCF of 38205 and 38210?

We will first find the prime factorization of 38205 and 38210. After we will calculate the factors of 38205 and 38210 and find the biggest common factor number .

Step-1: Prime Factorization of 38205

Prime factors of 38205 are 3, 5, 283. Prime factorization of 38205 in exponential form is:

38205 = 3³ × 5¹ × 283¹

Step-2: Prime Factorization of 38210

Prime factors of 38210 are 2, 5, 3821. Prime factorization of 38210 in exponential form is:

38210 = 2¹ × 5¹ × 3821¹

Step-3: Factors of 38205

List of positive integer factors of 38205 that divides 38205 without a remainder.

1, 3, 5, 9, 15, 27, 45, 135, 283, 849, 1415, 2547, 4245, 7641, 12735

Step-4: Factors of 38210

List of positive integer factors of 38210 that divides 38205 without a remainder.

1, 2, 5, 10, 3821, 7642, 19105

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38205 and 38210. The biggest common factor number is the GCF number.
So the greatest common factor 38205 and 38210 is 5.

Also check out the Least Common Multiple of 38205 and 38210